Properties

Label 1150.2.a
Level $1150$
Weight $2$
Character orbit 1150.a
Rep. character $\chi_{1150}(1,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $19$
Sturm bound $360$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1150.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(360\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1150))\).

Total New Old
Modular forms 192 34 158
Cusp forms 169 34 135
Eisenstein series 23 0 23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(14\)
Minus space\(-\)\(20\)

Trace form

\( 34 q - 4 q^{3} + 34 q^{4} - 4 q^{7} + 38 q^{9} + O(q^{10}) \) \( 34 q - 4 q^{3} + 34 q^{4} - 4 q^{7} + 38 q^{9} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} + 34 q^{16} + 8 q^{17} - 30 q^{19} - 6 q^{22} - 8 q^{26} + 8 q^{27} - 4 q^{28} - 24 q^{31} + 24 q^{33} - 16 q^{34} + 38 q^{36} - 6 q^{37} + 6 q^{38} + 8 q^{39} + 4 q^{41} + 32 q^{42} - 34 q^{43} + 6 q^{44} + 2 q^{46} + 24 q^{47} - 4 q^{48} + 2 q^{49} + 12 q^{51} - 4 q^{52} + 26 q^{53} - 12 q^{54} - 4 q^{56} + 48 q^{57} + 28 q^{58} - 16 q^{59} - 46 q^{61} + 4 q^{63} + 34 q^{64} - 28 q^{66} - 14 q^{67} + 8 q^{68} + 4 q^{69} + 32 q^{71} - 8 q^{73} - 10 q^{74} - 30 q^{76} + 16 q^{77} - 16 q^{78} - 4 q^{79} + 34 q^{81} - 4 q^{82} - 22 q^{83} - 34 q^{86} - 16 q^{87} - 6 q^{88} - 24 q^{89} - 48 q^{91} - 40 q^{93} - 16 q^{97} - 16 q^{98} + 34 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 23
1150.2.a.a 1150.a 1.a $1$ $9.183$ \(\Q\) None \(-1\) \(-2\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
1150.2.a.b 1150.a 1.a $1$ $9.183$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-3q^{11}+\cdots\)
1150.2.a.c 1150.a 1.a $1$ $9.183$ \(\Q\) None \(-1\) \(2\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots\)
1150.2.a.d 1150.a 1.a $1$ $9.183$ \(\Q\) None \(-1\) \(3\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+4q^{7}-q^{8}+\cdots\)
1150.2.a.e 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(-3\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-3q^{6}-4q^{7}+q^{8}+\cdots\)
1150.2.a.f 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(-2\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
1150.2.a.g 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-3q^{11}+\cdots\)
1150.2.a.h 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{7}+q^{8}-3q^{9}+2q^{11}+\cdots\)
1150.2.a.i 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(2\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
1150.2.a.j 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+(-1+\beta )q^{7}+\cdots\)
1150.2.a.k 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{17}) \) None \(-2\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+(-1+\beta )q^{7}+\cdots\)
1150.2.a.l 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+(3-3\beta )q^{7}+\cdots\)
1150.2.a.m 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{13}) \) None \(2\) \(-3\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
1150.2.a.n 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(0\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+(-3+3\beta )q^{7}+\cdots\)
1150.2.a.o 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{21}) \) None \(2\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(-1+\beta )q^{7}+\cdots\)
1150.2.a.p 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{17}) \) None \(2\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(1-\beta )q^{7}+\cdots\)
1150.2.a.q 1150.a 1.a $3$ $9.183$ 3.3.1101.1 None \(-3\) \(-1\) \(0\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
1150.2.a.r 1150.a 1.a $4$ $9.183$ 4.4.13448.1 None \(-4\) \(-3\) \(0\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(1+\beta _{3})q^{6}+\cdots\)
1150.2.a.s 1150.a 1.a $4$ $9.183$ 4.4.13448.1 None \(4\) \(3\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 2}\)